Two Particles P₁ and P₂ Are Moving in the Plane $x ^ { 2 } + y ^ { 2 } = 1$

question 7

Essay

Two particles p₁ and p₂ are moving in the plane, with p₁ moving vertically upward from initial point (0,0)and p₂ moving around the unit circle $x ^ { 2 } + y ^ { 2 } = 1$ with initial point (0, 1)in the counter-clockwise direction.
(a)Choose parameterizations for p₁ and p₂ so that the two particles collide at the point of intersection of their paths.
(b)If the sum of the speeds of these two particles is greater than 3 at the time of collision, then the two particles combine to become one.Will this happen with your chosen parameterization?

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